Two-dimensional and EM techniques for cross directional estimation and control

Cross directional monitoring and the control of sheet forming processes are treated as a two-dimensional (2D) dynamical systems issue. However, the sensors used in sheet forming processes do not usually collect the full two-dimensional information. Instead, a scanning sensor moves across the sheet in a zigzag manner, and it is this sparse data that must be used for monitoring and control. It is shown that EM methods can be used with a two-dimensional model for estimation and control by treating the unscanned area of the sheet as ´missing´ data. Particular attention is given to the efficient representation of the sheet forming process using state space models with suitable model order testing methods. Finally, it is shown how the EM model update is linked to a corresponding control algorithm.